To create a formula for the points (1, 5), (2, 7), (3, 9), and (4, 11), we need to determine the equation of the line that fits these points.
We'll start by checking the change in y-values and x-values to find the slope (m):
- For (1, 5) to (2, 7): change in y = 7 - 5 = 2; change in x = 2 - 1 = 1
- For (2, 7) to (3, 9): change in y = 9 - 7 = 2; change in x = 3 - 2 = 1
- For (3, 9) to (4, 11): change in y = 11 - 9 = 2; change in x = 4 - 3 = 1
Every point shows that the slope (m) is equal to 2.
Now, using the point-slope form of the line equation \(y = mx + b\), we will find the y-intercept (b). We can use any of the points we have, let’s use (1, 5):
\[ 5 = 2(1) + b \] \[ 5 = 2 + b \] \[ b = 5 - 2 = 3 \]
Thus, the equation of the line is:
\[ y = 2x + 3 \]
Now we can match this equation with the given options:
- 0 y = -2x + 3
- 0 y = 2x + 3 (Correct)
- 0 y = 2x - 3
- 0 y = -2x - 3
The correct formula for the points is:
y = 2x + 3